It's probably not the done thing, but as it's for family...
I get large insulated/EPS boxes with close fitting lids from a big local aquarium shop. They have fish delivered from around the world in them. The fish are in sealed plastic bags inside the containers so they aren't contaminated if the handlers are careful. If you wrap the bird in plastic bags, sealed as well as you can, or thoroughly wrapped in plastic sheeting and then seal the lid of the box with gaffer tape or similar, it'll almost certainly still be completely frozed by the time it arrives, but if it does thaw, it won't drip at all.
I send mine 24 hour delivery by local courier.